DEPARTMENT OF COMMERCE 



Scientific Papers 



OF THE 



Bureau of Standards 

S. W. STRATTON. Director 



No. 404 

magnetic reluctivity relationship as 

related to certain structures of 

a eutectoid-carbon steel 

BY 

C. NUSBAUM, Associate Physicist 
W. L. CHENEY, Assistant Physicist 
H. SCOTT, Assistant Physicist 
Bureau of Standards 



NOVEMBER 26, 1920 




PRICE, S CENTS 

told only by the Superintendeat of Documents, Government Printine Offic« 
Washington, T>. C. 

WASHINGTON 

GOVERNMENT PRINTING OFFICB 

1920 



DEPARTMENT OF COMMERCE 



Scientific Papers 



OF THE 



Bureau of Standards 

S. W. STRATTON, Director 



No. 404 

magnetic reluctivity RELATIONSfflP AS 

related to certain structures of 
a eutectoid-carbon steel 



BY 

C. NUSBAUM, Associate Physicist 
W. L. CHENEY, Assistant Physicist 
H. SCOTT, Assistant Physicist 
Bureau of Standards 



NOVEMBER 26, 1920 



PMCE, 5 CENTS 

Sold only by the Superintendent of Documents, Government Printing Office 
Washington, D. C. 

WASHINGTON 
GOVERNMENT PRINTING OFFICE ' 
1920 



A«- 



<^i* 



LIBRARY OF CONGRESS 
RECEIVED 

JAN10192I 

DOCUMENTS DIVISION 






< 



MAGNETIC RELUCTIVITY RELATIONSHIP AS RE- 
LATED TO CERTAIN STRUCTURES OF A EUTEC- 
TOID-CARBON STEEL 



By C, Nusbaum, W. L. Cheney, and H. Scott 



CONTENTS 

Page 

I. Introduction ' 739 

II. The reluctivity relationship 740 

1 . Definition of the term 740 

2. Stages of the magnetization and reluctivity curves 741 

3. Characteristics of the reluctivity line 742 

4. Pure materials 743 

5. Impure materials and complex structures 743 

(a) The parallel arrangement 744 

(6) The series arrangement 744 

I (c) The spheroidal arrangement 745 

(d) General arrangement 745 

III. Apparatus and heat treatment 746 

1 . Apparatus 746 

2 . Heat treatment 746 

IV. Experimental data 747 

V. Discussion and interpretation of results 753 

1. Precipitation of cementite 753 

2. Saturation and intercept values 753 

{a} Region A 753 

(b) Region B 756 

(c) Region C 756 

VI. Summary 757 

I. INTRODUCTION 

It is to the close relationship existing between the heat treat- 
ment and the magnetic properties ^ of iron and steel as well as 
between their heat treatment and mechanical properties, that 
magnetic analysis owes its promise of increasing metallurgical 
and industrial importance. Moreover, the magnetic and many 
other physical properties of iron and steel are greatly afifected by 
the thermal and mechanical treatments to which they are sub- 
jected during the process of manufacture. Changes in the physi- 
cal properties resulting from thermal treatment are generally 
considered as indicative of certain transformations and changes 
in structure. Such changes ^ have been discussed for the case of 
a I per cent carbon steel and it has been shown that a very rapid 

1 Maurer, Rev. de Mctallurgie, 6, p. 721; 1908. Burrows and Fahy, A. S. T. M. Proc, 19, p. s; 1919. 

2 C. Nusbaum, A. S. T. M. Proc, 19, p. 100; 1919. 

739 



740 Scientific Papers of the Bureau of Standards [Voi. i6 

rise of the maximum and residual induction and an even more 
pronOimced decrease in the coercive force occur between the 
drawing temperatiu-es of 150 and 250° C. Such changes very 
Hkely mark the transformation from martensite to troostite. 

While in all magnetic measurements at ordinary magnetizing 
forces the properties of a given specimen are always determined 
in the aggregate, measurements made in intense magnetizing 
fields have the added advantage of permitting a study of the 
reluctivity relationship. This relationship is valuable because it is 
capable of indicating the presence of one or more constituents 
and, therefore, gives promise of differentiating between differ- 
ent structures of carbon steels by magnetic methods, which is 
the purpose of the present paper. 

In this investigation a eutectoid-carbon steel (0.85 per cent 
carbon) has been chosen in order that the arrangement of the 
constituents may be as simple as possible. With suitable heat 
treatment there is no excess of ferrite or cementite to be rejected 
to the grain boundaries. Although this investigation has been 
limited to the one composition, the method is also applicable to 
the entire carbon series. 

II. THE RELUCTIVITY RELATIONSHIP 

1. DEFmiTION OF THE TERM 
The term "reluctivity" (p) is defined by the ratio 

where H is the magnetizing force and B the corresponding mag- 
netic induction or total flux density. For moderate values of the 
magnetizing force the relationship between the reluctivity (p) 
and the magnetizing force H is linear ^ and can be expressed by 
the equation 

p = a + ^H (2) 

where a and j8 are constants for a given material. For inductions 
resulting from very high magnetizing forces this linear equation 
no longer strictly holds, since the induction B does not approach 
a definite saturation value, but increases indefinitely; however, 

Bo=B-H 

approaches a finite saturation value, so that Kennelly's law 
applies not to B, but to Bo. The latter is usually called the 
metalHc induction, and may be considered as the magnetic flux 
carried by the molecules of the magnetic material not including 

• Kennelly, Am. Inst. Elect. Eng., Trans., 8, p. 485; 1891. 



Nusbaum, a^ney.-^ Magnetic Reluctivity of Eutectoid Steel 



741 



the flux H, carried by the space occupied by the material, but 
independent of it. The ratio 

^ = p, = a + m ^^^ 

is defined as the "metalHc reluctivity" and this linear relation 
holds for high magnetizing forces as well as for moderate ones. 
From now on in this paper the "metallic reluctivity" will be 
referred to simply as the reluctivity and will be designated by p. 

2. STAGES OF THE MAGNETIZATION AND RELUCTIVITY CURVES 

In Fig, I are plotted the (i) magnetization and (2) reluctivity 
curves for an eutectoid-carbon steel quenched in water. The 



ytJf—3-*f 



20000 




80 m no /40 /bo .'SO zoo zzo Z'fo 260 230 

Fig. I. — Magnetization and, reluctivity curves for eutectoid carbon steel quenched in water 

general shape of the curves is that characteristic of a steel of 
high carbon content and in a hardened condition. The three 
stages of the curves are designated by the letters A, B, and C. 
In stage A of the magnetization curve the relation between the 
induction B and the magnetizing force H is nearly a linear one 
and the slope of the curve depends on the state of the material, 
being generally steep for soft and more gradual for magnetically 
hard materials. The molecular magnets have been distturbed only 
slightly relative to their original condition of stable equilibrium. 
In stage B the groups of molecular magnets pass from their 



742 Scientific Papers of the Bureau of Standards [Voi. i6 

previous condition of stability through an unstable state into a 
new position of stability. In magnetically soft substances this 
change in molecular stability within the various groups takes 
place almost simultaneously, and the slope of the magnetization 
curve is correspondingly steep. In magnetically hard substances 
this change occurs during a longer interval, and thus the slope 
of the ctirve is more gradual. In stage C the alignment of the 
molecular groups approaches more and more the direction of the 
magnetizing force as it increases in magnitude. The slope of 
the curve decreases in magnitude. 

However, the last stage becomes more significant when use 
is made of the reluctivity relatioriship represented for the same 
substance by the curve (2) . It is for this stage that equation (3) 
accurately holds. Stages A and B can not be represented generally 
by any such simple relationship. For magnetically homogeneous 
and soft substances these two stages practically disappear, while 
for magnetically hard substances they become increasingly 
pronounced. 

Steinmetz,^ however, has suggested that both of these are 
stages of instability, and that, if the specimen whose magnetic 
properties are being determined is simultaneously subjected to 
vibration or to an alternating magnetic field applied at right 
angles to the unidirectional field /#, these two characteristic 
stages practically vanish ; that it is probable that the stable relation 
between the field intensity H and the flux density B is expressed 
over the entire range from zero to infinity by the above Hnear 
relationship. 

3. CHARACTERISTICS OF THE RELUCTIVITY LINE 

In equation (3) a is the intercept of the linear portion of the 
curve extended to intersect the axis of ordinates, as shown in 
Fig. I, and is generally designated as the coefficient of magnetic 
hardness. If the intensity of magnetization and the susceptibility 
are represented by / and K, respectively, it can be shown easily 
that 

so that the reciprocal of the susceptibility also bears a Unear 
relationship to the magnetizing force. The ordinates of the 
reciprocal of the susceptibility are evidently /[ir times those of the 
reluctivity curve. Also, if in equations (3) and (4) H is allowed 

* Steinmetz, Gen. Elect. Rev., 20, p. 135; 1917. 



Nusbaum. Cheney.-^ Magmtic RelucHvity of Eutectoid Steel 



743 



to increase indefinitely Bo and / approach their saturation or 
maximum values B^ and Jm, respectively, so that 



58=3 and 7m = ^, 



(5) 

The constants /S and /S' are thus called the coefficients of saturation 
of the metallic induction and intensity of magnetization, respec- 
tively. Low values of these constants represent high -saturation 

values. 

4. PURE MATERIALS 

For pure and well-annealed materials, such as Norway, Swedish 
charcoal, and electrolytic iron, the p—H relation is a straight line. 
This straight-line relationship is well illustrated by the ajlmirable 
experiments of B. O. Peirce ^ on various kinds of pure iron. Fig. 




/ooc. ;joc. 200O. 



^doA 



Fig. 2. — Reciprocal of susceptibility for "American ingot iron" (B. O. Peirce) 

2, taken from Peirce's paper, shows the iiK — H line for a speci- 
men of "American ingot iron." 

5. IMPURE MATERIALS AND COMPLEX STRUCTURES 

In the more or less impure commercial materials the p—H rela- 
tion, although an approximately straight line, generally has one, 
and occasionally two, points where its slope changes. Since the 
change in slope of the line is in general greater with increase in 
impurity of the material, the cause evidently is lack of homo- 
geneity; that is, the presence in the substance as aggregates or 
conglomerates of materials of different magnetic characteristics, 

* B. O. Peirce, Proc. Amer. Acad. Arts and Sci., 19, June, 1913. 



744 Scientific Papers of the Bureau of Standards [Voi. i6 

such as cementite, silicide, etc. Such bodies generally have a 
much greater magnetic hardness and a lower saturation value, and 
give, therefore, the observed effect. 

In carbon steel the arrangement of the constituents, such as 
pearlite and ferrite or pearlite and cementite, depends on the car- 
bon content and also on its previous mechanical and thermal treat- 
ment, and is generally a random one. However, as magnetic cir- 
cuits the arrangement of these constituents may be considered as 
combinations of any of three simple arrangements, viz, (a) the 
parallel, (6) the series, and (c) the spheroidal. 

(a) The Parallel Arrangement. — ^This arrangemen:t is the easiest 
for experimental verification and also for mathematical proof. An 
ideal parallel arrangement would be, if the alternate layers of ce- 
mentite and ferrite in the pearlite grains of a eutectoid steel were 
all parallel to each other and to the direction of the effective mag- 
netic field. If, then, Pi and P2. and a^ and 02 are the reluctivities 
and cross-sectional areas of the two constituents, respectively, the 
resultant reluctivity p is given by the relation 

P1P2 ^ ,^. 

^ Pi a^ +P2 ai *- '' 

The reluctivity curve for two constituents in parallel approximates 
to two straight lines joined by a bend. This has been experiment- 
ally verified by Ball," using pure iron and cobalt in a closed mag- 
netic circuit. 

(&) The Series Arrangement. — An ideal series arrangement would 
be if all of the lamellae of ferrite and cementite in the pearlite grains 
of eutectoid steel were oriented parallel to each other and per- 
pendicular to the direction of the effective magnetic field. If the 
reluctivities, lengths, and effective cross-sectional areas of the two 
constituents are, respectively, Pi, pj, h, I2, ^i, and aa, the resultant 
reluctivity is expressed by the equation 

h +I2 Pi h , P2 4 , . 

p~ir^^^~^ - (7) 

where a is the equivalent cross-sectional area. The resultant re- 
luctivity line consists of two or more approximately straight lines 
joined by more or less marked bends. The series arrangement 
can not be experimentally verified, since it is practically impossible 
to make satisfactory magnetic joints between the two materials. 
The solution can, however, be approximately obtained by a graph- 

5 Ball, Jour. Frank. Inst., 181, p. 481; 1916. 



sc"« ""'"• ^*'"'''"] Magnetic Reluctivity of Eutectoid Steel 745 

ical method first outlined by J. and E. HopkinsonJ. The reluc- 
tivity is always greater in magnitude for the series than the parallel 
arrangement for a given ratio of the constituents. 

(c) Spheroidal Arrangement. — The third arrangement may, for 
want of a better term, be called the spheroidal arrangement. It 
is well illustrated in a low-carbon (o.i per cent) steel where the 
pearlite is distributed throughout the ferrite in irregularly shaped 
masses approximating in a general way to spheres or ellipsoids. 
The spherical masses (hard magnetically) carry practically no 
flux at low field intensities, all the flux being carried by the 
surrounding soft material. As the flux-carrying material occupies 
only part of the space, the flux density therefore rises rapidly, 
giving low a, and tends toward an apparent low-saturation value. 
At higher field intensities the spherical masses begin to carry flux. 
While in the softer material the flux increases at a lesser rate the 
increase of flux in the spherical masses gives a greater increase 
of the total flux density and a greater saturation value, but also 
a greater hardness, as the result of both materials. There is thus, 
in this arrangement, as well as in the others, a bend in the reluc- 
tivity line. 

A special, but a very important, case is the distribution of very 
finely divided magnetic particles throughout a magnetically softer 
medium. If the particles are ultra microscopic in size, the medium 
is not only homogeneous but isotropic as well. It is also quite 
probable that the individual crystals would be composed of the 
two constituents rather than each crystal consisting of only one 
constituent. In the former arrangement the "intrinsic " magnetic 
field of the more magnetic of the constituents would entirely 
dominate the field of the weaker, so that the material would 
conduct itself as if magnetically homogeneous, and the reluctivity 
line would be a straight one. 

{d) General Arrangement. — The arrangement of the constituents 
of a carbon steel as a function of the carbon content and the 
orientation of the respective grains is a random one. However 
complex the arrangement is, it may generally be considered as 
different combinations of any of the above simple arrangements. 

' J. and E. Hopkinson, Pliil. Trans., 1886; p. 331. 
13829°— 20 2 



746 Scientific Papers of the Bureau of Standards [voi. 16 

III. APPARATUS AND HEAT TREATMENT 

1. APPARATUS 

' In order to obtain values of the magnetic flux or intensity of 
magnetization which approach saturation, it is necessary to use 
high values of the magnetizing force. The apparatus suitable for 
this purpose and used in this investigation has already been 
described.* 

2. HEAT TREATMENT 

Two specimens (22 cm long) of eutectoid-carbon steel whose 
chemical analysis showed the following compositions were selected 
and turned down to a uniform diameter of approximately 7 mm: 



C. .. 

Mn. 
Si.. 



Per cent 

• 0.85 
■ -23 

• -23 



Cr. 
P. 

S., 



Per cent 
■ O. OS 
. 016 
. 014 



Each of these specimens was quenched from a temperature of 
800° C — one in a fairly Hght oil and the other in water at room 
temperature — and then carefully ground down to a uniform 
diameter of 6 mm. Induction tests showed that both specimens 
were magnetically imiform along their entire length. Each speci- 
men was then cut into halves, designated as A and B, respectively, 
and the resulting ends ground, polished, and examined microscop- 
ically. The structure of both specimens was martensitic. The 
two halves of each rod were then drawn alternately to increasingly 
higher temperatures, as indicated in Table i, and the normal 
induction curves determined after each operation. The specimens 
were kept at the designated drawing temperatures for a period of 
half an hour each, the water- quenched specimens being air cooled 
and the oil-quenched ones cooled in lime. 

TABLE 1. — Drawing Temperatures (Degrees Centigrade) 



Oil-quenched specimen 

Water-quenched specimen. 



f A 


100 


200 


250 


300 


410 


475 


600 


I B 


170 


230 


270 


370 


450 


500 


700 


I •*■ 


100 


200 


250 


300 


400 


450 


500 


1 B 


170 


230 


270 


350 


430 


470 


600 



700 



8 W. X,. Cheney, B. S. Sci. Papers, No. 361; 1920. 



Nusbaum, Cheney, "X 
Scott i 



Magnetic Reluctivity of Eutectoid Steel 



747 



IV. EXPERIMENTAL DATA 

In Fig. 3 are represented several magnetization curves as illus- 
trative of this particular type of steel on being quenched in water 
from 800° C and drawn in steps to increasingly higher tempera- 
tures. The data for curve i are displayed in Table 2 , so that one 
may have a clearer idea of the actual observations from which the 
curve was plotted. Tables 3 and 4 show, in a condensed form, 
the data corresponding to all heat treatments. The values of 




/so 200 



zso 



xo 



Fig. 3. — Magnetization curves Jor eutectoid carbon steel, quenched in water and drawn 

the induction therein shown are not in all cases the actual observed 
values, but are interpolated from the curves for definitely chosen 
values of the magnetizing force [H). Curves for many of the 
intermediate drawing temperatures are omitted, and only those 
possessing distinctive features are given. Since the specimens are 
of small diameter and the rates of quenching are thus not markedly 
different, the curves for the oil-and-water-quenched specimens are 
similar though not identical. 



748 



Scientific Papers of the Bureau of Standards 



[Vol. i6 



TABLE 2. — Magnetic Properties of 0.85 per cent Carbon Steel Quenched in Water 

from 800° C 



H 


B 


/ 


ilK 


M 


H 


B 


/ 


lIK 


V- 


14 


540 


42 


0.335 


38.6 


535 


15 960 


1225 


0.437 


29.8 


30 


1 320 


102 


.293 


44.0 


685 


16 660 


1268 


.540 


24.3 


56 


3 880 


304 


.184 


69.3 


860 


17 300 


1305 


.658 


20.1 


88 


8 040 


631 


.140 


91.4 


1090 


17 900 


1335 


.817 


16.4 


118 


10 220 


800 


.148 


86.6 


1380 


18 570 


1364 


1.012 


13.5 


156 


11 700 


916 


.170 


75.0 


1710 


19 100 


1380 


1.240 


11.2 


232 


13 250 


1034 


.224 


57.1 


2000 


19 520 


1390 


1.440 


9.8 


318 


14 400 


1118 


.284 


45.3 


2420 


20 150 


1407 


1.720 


8.3 


430 


15 320 


1182 


.364 


35.6 


2630 


20 440 


1414 


1.860 


7.8 



TABLE 3. — Induction for Given Magnetizing Forces after Quenching Specimen of 
of 0.85 per cent Carbon Steel in Water and after Drawing to Successively Higher 
Temperatures 





Induction (B) 


H 


Water 
quenched 


102° C 


170° C 


200° C 


230° C 


250° C 


270 C° 


300° C 


20 


780 
3 180 
9 150 

11 500 

12 700 

14 250 

15 700 

16 700 

17 650 

18 800 

19 600 

20 250 


700 
3 050 
8 750 

11 250 

12 450 

14 000 

15 750 

16 700 

17 700 

18 800 

19 650 

20 300 


840 
3 550 
9 000 

11 200 

12 370 

13 700 

15 250 

16 050 

16 850 

17 800 

18 600 

19 250 


950 

5 350 

11 600 

13 500 

14 600 

15 600 

16 800 

17 500 

18 250 

19 150 

19 800 

20 400 


2 200 
9 900 

14 360 

15 900 

16 500 

17 900 

18 940 

19 500 

20 100 

20 900 

21 500 

22 000 


3 800 
13 650 

16 600 

17 820 

18 500 

19 300 

20 100 

20 500 

21 000 

21 800 

22 400 
22 800 


2 400 
13 400 

16 580 

17 830 

18 500 

19 300 

20 100 

20 600 

21 100 

21 800 

22 300 
22 800 


3 700 


50 


14 350 


100 


16 900 


150 


18 000 


200 


18 570 


300 


19 300 


500 


19 900 


700 


20 300 


1000 


20 800 


1500 


21 500 


2000 


22 100 


2500 


22 600 







H 


Induction (B)— Continued 


370° C 


410° C 


450° C 


475° C 


500° C 


600° C 


700° C 


20. .. 


3 500 
14 350 

16 900 

17 700 

18 200 

19 000 
19 500 

19 950 

20 380 

21 050 

21 650 

22 220 


3 900 
15 000 

17 050 

18 000 

18 500 

19 100 

19 750 

20 200 

20 700 

21 400 

21 950 

22 400 


3 000 
14 250 

16 800 

17 600 

18 080 

18 800 

19 500 

19 900 

20 400 

21 100 
21 400 
21 900 


2 600 
13 450 

16 500 

17 500 

18 000 

18 800 

19 700 

20 100 

20 570 

21 200 

21 700 

22 130 


1 550 
12 650 

16 070 

17 080 

17 650 

18 450 

19 250 

19 720 

20 300 

21 000 

21 600 

22 120 


7 500 
14 100 

16 200 

17 170 

17 620 

18 250 

19 150 

19 700 

20 300 

21 000 

21 650 

22 250 


7 000 


50 .. 


13 350 


100 


15 100 


150 . .... 


15 900 


200 


16 400 


300 


17 100 


500 


18 000 


700 


18 600 


1000 


19 200 


1500 


20 000 


2000 


20 700 


2500 


21 200 







Nusbaum. ckeney.-j Maguetic Reluctivity of Eutectoid Steel 



749 



TABLE 4. — Induction for Given Magnetizing Forces After Quenching Specimen of 
0.85 per cent Carbon Steel in Oil and After Drawing to Successively Higher 
Temperatures 





Induction (B) 


H 


on 

quenched 


100° C 


170° C 


200° C 


230° C 


250° C 


270° C 


300° C 


20 


700 
3 250 
8 950 

11 380 

12 750 

14 050 

15 550 

16 500 

17 450 

18 580 

19 350 

20 000 


900 
3 300 
8 900 

11 450 

12 700 

13 950 

15 550 

16 550 

17 500 

18 550 

19 380 

20 100 


1 300 

4 850 

10 450 

12 520 

13 630 

14 900 
16 050 

16 850 

17 650 

18 620 

19 400 

20 100 


1 200 

5 850 

U 400 

13 230 

14 220 

15 320 

16 660 

17 420 

18 250 
14 150 

19 900 

20 600 


1 550 
9 600 

14 370 

15 900 

16 850 

17 950 

19 460 

20 220 

20 850 

21 630 

22 280 
22 800 


2 350 
12 750 

16 300 

17 450 

18 150 

19 100 

20 200 

20 700 

21 250 

22 000 

22 600 

23 150 


2 350 
12 920 
14 950 
17 120 

17 700 

18 350 

19 380 

19 750 

20 200 

20 900 

21 420 
21 920 


5 6S0 
14 000 

16 630 

17 700 

18 250 

18 850 

19 650 

20 150 

20 700 

21 400 


SO.. 


100 


150 


200 


300 


500 


700 


1000 


1500 


2000 


21 950 

22 400 


2500 






H 


Induction (-B)— Continued. 


350° C 


400° C 


430° C 


450° C 


470° C 


500° C 


600° C 


700° C 


20 


3 550 
14 350 

16 560 

17 400 

18 000 

18 900 

19 400 

19 900 

20 360 

21 050 

21 660 

22 250 


3 550 
14 450 

16 580 

17 550 

18 050 

18 650 

19 400 

19 880 

20 400 

21 100 

21 650 

22 120 


3 550 
14 650 

16 800 

17 650 

18 150 

18 800 

19 500 

20 000 

20 500 

21 200 

21 750 

22 200 


2 850 
14 250 

16 600 

17 400 

18 100 

19 100 
19 250 

19 900 

20 400 

21 100 

21 650 

22 150 


2 750 
13 850 

16 450 

17 420 

18 000 

18 750 

19 180 

19 650 

20 120 

20 850 

21 500 

22 050 


3 350 
13 950 

16 250 

17 120 

17 700 

18 550 

19 300 

19 720 

20 250 

21 000 

21 620 

22 200 


4 000 
13 650 

15 870 

16 800 

17 300 

18 000 

18 900 

19 400 

20 020 

20 700 

21 450 

22 050 


7 100 


50 


14 050 


100 


15 700 


150 


16 450 


200. .■: 


16 950 


300 , 


17 600 


500 


18 700 


700 


19 250 


1000 


19 850 


1500 


20 680 


2000 


21 350 


2500 


21 950 







The successive drawing operations produce an increasing steep- 
ness in the second stage of the curve, indicating that the material 
is becoming increasingly softer magnetically. The third stage of 
the curve is increasingly greater in magnitude for lower but not for 
intermediate or high drawing temperatures, as is illustrated by 
the crossing of the curves 3,4, and 5 of Fig. 3. This decreasing in 
magnitude of the saturation intensity is evidently due to a rear- 
rangement of the constituents. While such curves are valuable 
as criteria of the heat treatment, yet they often are dif&ctilt to 
interpret. 

In Fig. 4 the values of the induction for constant values of the 
magnetizing force are plotted as ordinates against the drawing 
temperatvires as abscissae. The agreement between the respective 
values of the induction for the two specimens is generally quite 



750 



Scientific Papers of the Bureau of Standards 



[Vol. i6 



good except for low and high drawing temperatures. Special 
attention is called to the very rapid rise of the induction for the 
drawing- temperatiure intervals 200 to 250° C, the significance of 
which will be discussed later. 

The reciprocal of the susceptibility I ^ j is plotted against the 

magnetizing force in Fig. 5 for the water-quenched specimens in 




wooo-. 



Fig. 4.- 



/do' 200' 3O0' 400' SCO' 600° 700" ^00' 
OjisAw/Ncr TeM^£/?ATOjee ^ £}e<r- ce/sir. 

-Variation of induction for a given magnetizing force 
with the drawing temperatures 



four conditions of treatment, viz, (i) quenched, (2) drawn to 250°, 
(3) to 370°, and (4) to 700° C. Cmrves i and 4 consist of two 
straight lines joined by a bend a. The lower part of each ciurve 
is extended so as to show more clearly the indicated bend. The 
curves 2 and j are straight lines throughout their entire third stage. 
Table 2 shows the values from which ciurve i was plotted, while 
Tables 5 and 6 show the reciprocal of the susceptibility for the 
other heat treatments. The statements made with reference to 
Tables 3 and 4 also apply to this case. 



Nusbaum, Clieney,! 
Scott J 



Magnetic Reluctivity of Eutectoid Steel 



751 




SCO /OOO /SOO ZOOO 2 500 .UX3C' 

Fig. 5. — Reciprocal of susceptibility for eutectoid carbon steel, quenched in water and drawn 

TABLE 5. — Reciprocal of Susceptibility for Given Magnetizing Forces After Quench- 
ing Specimen of 0.85 Per Cent Carbon Steel in Water and After Drawing to Succes- 
sively Higher Temperatures 



H 


Reciprocal of susceptibility (ilK) 


Quenched 


102° C 


170° C 


200° C 


230° C 


250° C 


270° C 


300° C 


20 


0.320 

.200 

.145 

.165 

.2QP 

.270 

.413 

.550 

.760 

1.098 

1.435 

1.785 


0.340 

.220 

.150 

.180 

.212 

.277 

.413 

.548 

.750 

1.085 

1.425 

1.770 


0.270 

.200 

.138 

.175 

.210 

.275 

.435 

.580 

.800 

1.163 

1.525 

1.890 


0.240 

.120 

.110 

.142 

.180 

.250 

.390 

.530 

.735 

1.078 

1.420 

1.770 


0.120 
.070 
.090 
.120 
.155 
.220 
.345 
.475 
.665 
.980 
1.300 
1.620 


0.070 
.050 
.078 
.108 
.138 
.200 
.320 
.442 
.630 
.940 
1.245 
1.555 


0.100 
.048 
.078 
.110 
.140 
.200 
.322 
.445 
.630 
.935 
1.240 
1.550 


0.065 


50 


.045 


100 


.075 


150 


110 


200 


. 140 


300 


.200 


500 


.325 


700... 


.450 


1000 


.640 


1500 : 


.955 


2000 


1.270 


2500. . 


1.585 













Reciprocal of susceptibility (r/i')— Continued 


H 


370° C 


410° C 


450° C 


475° C 


500° C 


600° C 


700° C 


20 


0.055 
.045 
.080 
.110 
.140 
.205 
.332 
.460 
.650 
.968 
1.283 
1.605 


0.065 
.046 
.080 
.110 
.140 
.205 
.330 
.455 
.642 
.968 
1.270 
1.590 


0.085 
.040 
.080 
.110 
.140 
.208 
.335 
.460 
.660 
.980 
1.300 
1.625 


0.100 
.050 
.078 
.110 
.140 
.205 
.332 
.460 
.650 
.970 
1.288 
1.610 


0.160 
.055 
.080 
.112 
.145 
.210 
.340 
.465 
.655 
.970 
1.290 
1.608 


0.045 
.046 
.080 
.110 
.145 
.210 
.340 
.465 
.655 
.970 
1.282 
1.595 


0.050 


50 


.050 


100 


.083 


150 


.120 


200 


.155 


300 


.225 


SOO 

700 

1000. . 


.370 
.500 
.700 


1500 


1.025 


2000 ., 

2500 


1.355 
1.680 







752 



Scientific Papers of the Bureau of Standards 



[Vol. i6 



TABLB 6. — Reciprocal of Susceptibility for Given Magnetizing Forces After Quench- 
ing Specimen of 0.85 per cent Carbon Steel in Oil and After Drawing to Succes- 
sively Higher Temperatures 



H 




Reciprocal of susceptibility 


iim 






Quenched 


100° c 


170° C 


200° C 


230° C 


250° C 


270° C 


300° C 


20 


0.332 

.215 

.145 

.165 

.200 

.275 

.425 

.560 

.770 

1.115 

1.460 

1.805 


0.300 

.200 

.145 

.170 

.208 

.278 

.420 

.560 

.766 

1.110 

1.450 

1.795. 


0.188 

.145 

.115 

.152 

.188 

.260 

.405 

.546 

.755 

1.105 

1.450 

1.800 


0.225 

.115 

.108 

.142 

.180 

.250 

.392 

.525 

.730 

1.068 

1.405 

1.742 


0.150 
.070 
.090 
.122 
.150 
.212 
.333 
.455 
.628 
.940 
1. 245- 
1.555 


0.105 
.050 
.070 
.110 
.140 
.200 
.320 
.440 
.623 
.925 
1.228 
1.530 


0.105 
.045 
.078 
.108 
.140 
.205 
.335 
.465 
.655 
.978 
1.300 
1.620 


0.060 


50 


.042 


100 


.075 


150 


.107 


200 : 


.140 


300 


.200 


500 


.325 


700 


.450 


1000 


.640 


1500 


.955 


2000 


1.265 


2500 


1.585 







H 




Reciprocal of su 


sceptibility (ilK) 


—Continued 




350° C 


400° C 


430° C 


450° C 


470° C 


500° C 


600° C 


700° C 


20 


0.060 
.048 
.080 
.110 
.142 
.205 
.332 
.460 
.650 
.968 
1.284 
1.605 


0.060 
.045 
.078 
.110 
.142 
.207 
.335 
.460 
.650 
.968 
1.285 
1.605 


0.070 
.048 
.078 
.110 
.140 
.205 
.330 
.457 
.648 
.965 
1.278 
1.595 


0.075 
.040 
.080 
.112 
.145 
.210 
.335 
.460 
.655 
.970 
1.285 
1.605 


0.115 
.048 
.080 
.110 
.145 
.210 
.340 
.468 
.658 
.975 
1.290 
1.610 


0.075 
.048 
.080 
.110 
.145 
.210 
.340 
.468 
.655 
.970 
1.285 
1.600 


0.085 
.045 
.080 
.110 
.145 
.210 
.340 
.468 
.665 
.980 
1.295 
1.615 


0.040 


50 


.045 


100 


.078 


150 


.115 


200 

300 


.147 
.215 


500 


.350 


700 


.475 


1000 


.668 


1500 


.980 


2000 : 


1 300 


2500 


1.620 







As has been previously suggested, the saturation value of the 
intensity of magnetization can be calculated from the relation 

I 



/m = 



^ 



where /S is the slope of the^ — // line. If the line consists of two 

lines joined by a bend there are two values of /3. The greater of 
these slopes is the "apparent" saturation value while the lesser 
is the "true" saturation value for the material. 

In Fig. 6 the saturation values of the intensity of magnetiza- 
tion are plotted against the drawing temperature as the inde- 
pendent variable. The real saturation values are indicated in 
full lines, while the apparent values are in broken lines. . In Fig. 7 
the intercepts (a) are plotted and represented in a similar manner. 



Nusbaum. Cheney^ Magnetic Reluctivity of Eutectoid Steel 753 

V. DISCUSSION OF THE RESULTS 
1. PRECIPITATION OF THE CEMENTITE 

The significance of the very rapid rise of the induction within 
the tempera tiu-e hmits of 150 and 250° C has aheady been dis- 
cussed, as relating to a i per cent carbon steel,® in a previous 
paper. However, for the sake of completeness the essential points 
will be given briefly. 

According to Tammann's^° law for solid solutions, the intensity 
of magnetization of a solid solution is less than that of the more 
magnetic of the two constituents and also less than would be 
calculated from a knowledge of the proportion of the constituents. 
This is well illustrated by the difference in induction (Fig. 4) for 
the material when in the quenched condition and drawn to 250° 
C. The experiments of Honda ^^ on the magnetic transformation 
of cementite in quenched carbon steels are additional evidence. 
Cementite is approximately one-tenth as magnetic as pure iron 
and becomes nonmagnetic at 2 1 5 ° C. As a quenched high-carbon 
steel is repeatedly drawn to increasingly higher temperatures, the 
magnitude of the magnetic transformation of cementite increases 
and reaches its maximum in the neighborhood of 300° C. 

These experimental facts indicate that in a martensitic struc- 
ture the cementite is in solid solution and is precipitated within 
the drawing- temperature interval of 150 to 250° C. The magnetic 
changes on tempering accompanied by heat evolution ^^ at least 
represent the completion of a suppressed transformation, which 
completion may be considered as the transition from martensite 
to troostite. Whether such a criterion is acceptable remains for 
the future to decide. 

2. SATURATION AND INTERCEPT VALUES 

The regions A, B, and C of Figs. 6 and 7 show the existence of 
three magnetically differentiable arrangements or structures very 
probably of martensite, troostite, and sorbite, respectively. 

(a) Region A . — The fact that there is a break in the reluctivity 
line throughout this entire region indicates that two magnetically 
different constituents are present. This may be due to one of 
two factors, or both, namely, the stresses in the steel or the 
existence of two physically different constituents. 

' Nusbaum, A. S. T. M. Proc, 19, p. loo; 1919. 
10 Tammann, Zeit. fur Phys. Chem., 65, p. 79; 1908. 
•' Honda, Tohoku University Repts., 6, p. 149; 1917. 
" Scott and Movius, B. S. Sci. Papers, No. 396; 1920. 



754 



Scientific Papers of the Bureau of Standards 



[Vol. i6 



Owing to the stresses set up during the quenching process, a 
quenched material is always in a state of strain. The outside 
portion of the material is in a state of tension, while the inside 
portion is in a state of compression. The efifect of tension ^^ 
is in general to increase the induction at low field intensities and 
decrease it at high intensities relative to that of the material in 
the unstressed state. The stressed material thus acts as a mag- 





V. 




A 










a 




1 






^ 




! 












1 










1 








1 


je A/M. 




















1 

t 






















I 




X 







K 










> 


















1 1 










^-1 


i 


"■■~~^ 








■ 




, 


^ 


/ 


/ 

/ 




















•^^. 


tAAflA. 








V 


; 

/ 
1 










1 














,''' 


^'^ 


h""-' 




1 
1 










1 


a/^ 


1 1 

QU£NCH£0 

1 r 




/3eoo- 










■i.. 























i 
i 



;0O iOO JOO 400 X>0 660 700 




/3 0(X>- 

fOO 200 JOO 400 SOO 600 70O 

Fig. 6. — Variation of maximum intensity of m,agnetization with drawing temperature 

netically softer substance of lower maximum intensity of mag- 
netization. Its reluctivity line would have a lower intercept 
and a higher slope when in the stressed (tension) state than when 
in the normal state. Under compression " the induction is lower 
in value at low field intensities than for the material in the normal 
state. Thus, under compression, the material conducts itself as 
a magnetically harder substance, and probably approaches a 

13 Villari, Pogg. Ann.; i868. Honda and Shimizu, Phil. Mag., 4, p. 388: 1903. 
I* Smith and Shennan, Phys. Rev., 4, p. 267; 1914. 



Nusbaum, Cheney,'] 
Scott J 



Magnetic Reluctivity of Eutectoid Steel 



755 



higher saturation value. Its reluctivity line would have a higher 
intercept and also, probably, a lower slope under compression 
than in the normal state. In a material in a quenched state the 
exterior portions are thus magnetically softer and have a relatively 
lower saturation value than the interior portions, and there is a 
gradual transition from the one to the other. Such an arrange- 
ment corresponds to a complex parallel-series arrangement of 









— A 




1 






^ — 








— c — 




»t 




' — ■ 




\ 




1 






























s. 


























y 






\ 


1 










1 












0.06 






^ 


\ 

\ 


\ 








c 


1 ■ 

VL 6 


xue^ 


<c/-fa 

















N 


Ai 










1 
1 












0.0^ 




















1/^ 










■ 


















^ 


\ 






- „> 


r 














s 


JC 


w 


2 


00 

1 


Jt 


fQ 7 


4t 




1 


/pea- 




r. 


76 


9 


\ 


^-. 




















1 
1 












K 


~ 


^' 


^v 


-\ 














1 

1 
1 














.'-' 




'> 


\ 












1 

1 
































V 


VATSi 


' GUI 


fUCHt 


'D 






C,03 








\ 


\ 












^ — 








■ 












\ 


\ 










1 






^ 






001- 










\ 


V 








|/ 






















-^ 










1 
1 













too 



zoo 



400 ^00 600 ;i>o 



soo 

Fig. 7. — Variation of the coefficient of magnetic hardness (intercept) with drawing 

temperature 



materials of imiformly varying magnetic properties. From earlier 
arguments in this paper it is thus evident that there should be 
a break in the reluctivity line for a quenched material. Drawing 
the material so as to relieve the strains should thus decrease the 
change in slope and also decrease in magnitude the difference 
between the apparent and the true satiuration values of the in- 
tensity of magnetization. While the stresses in the material 



756 Scientific Papers of the Bureau of Standards [Voi. 16 

undoubtedly contribute to the effects observed, they very hkely 
are not the only cause, or perhaps not even the predominating 
one. It is not probable that the strains are entirely removed at 
a temperature of 250° C. The questions here raised can be 
answered only by further experimentation. 

(6) Region B. — ^Throughout this entire drawing- temperature 
interval the steel behaves like a magnetically pure material. 
However, the experiments of Honda ^^ show quite clearly that the 
carbon present in this region is in the form of cementite. Since 
there are thus two magnetic constituents present, in order that 
the material in its entirety may be magnetically homogeneous 
according to the arguments in the earlier part of the paper, the 
cementite is evidently distributed very uniformly in very finely 
divided particles (ultra microscopic in size) throughout the entire 
mass of the ferrite, and there are no separate cementite and ferrite 
crystals. This agrees with the conception of troostite generally 
accepted b)^ metallographists and first presented by Benedicks. 
Throughout this entire region the maximum intensity of magnet- 
ization generally gradually decreases in magnitude, while the 
intercept values remain constant. 

(c) Region C. — With increasing drawing temperatures the ultra 
microscopic particles of cementite of region B form aggregates of 
continually increasing size, which finally attain such dimensions 
as to produce a magnetically nonuniform or inhomogeneous mate- 
rial, as is indicated by a more or less marked break in the reluc- 
tivity Une. The line of demarcation netween regions B and C 
then marks the transition between the regions of magnetic homo- 
geneity and nonhomogeneity. Since this transition is so sharply 
defined, it may be chosen as the beginning of the metallographic 
constituent sorbite. Beyond this transition point as the aggregate 
particles or conglomerates either increase in size with increasing 
drawing temperatures or as the medium approaches more and 
more toward stratification the bend in the reluctivity line becomes 
more pronounced, as is indicated by the increasing magnitude of 
the difference between the apparent and real saturation values of 
the intensity of magnetization and also the intercept values. 

'5 Honda, Tohoku, Univ. Reports, 6, p. 149; 1917. 



Nusbaum, Cheney. j Magnetic Rcluctivity of Eutectoid Steel 757 

VI. SUMMARY 

The essential and important points of this paper may be sum- 
marized as follows : 

1. The very rapid rise of the maximum induction in the tem- 
perature interval of 150 to 250° C, accompanied by heat evolution, 
viewed in the light of Tammann's law and Honda's experiments, 
indicates that the cementite in this temperature interval is thrown 
out of solid solution, and thus that in martensite the cementite is 
in solid solution. It also indicates the completion of a previously 
suppressed transformation, which completion may be considered 
as the beginning of the metallographic constituent troostite. 

2. The magnetic inhomogeneity within the region A may be 
due to one of two causes or both, viz, (i) the presence of another 
constituent, (2) the stresses set up in the material during the 
quenching operation. The stresses undoubtedly play an impor- 
tant part, but are not necessarily the predominating factor. 

■3. In region B the material is magnetically homogeneous. This 
fact is not an experimental verification, but is evidence in favor of 
Benedicks's theory of troostite. 

4. In region C the material is magnetically nonhomogeneous. 
This inhomogeneity is due to the increasing size of the aggregates 
and to their approaching stratification. 

5. The transition point between regions B and C may be con- 
sidered as the beginning of the metallographic constituent sorbite. 

6. The magnetic reluctivity relationship provides a method for 
magnetically differentiating the metallographic constituents of the 
carbon-iron series. 

Credit is due to H. A. Wadsworth for most of the heat treating. 

Washington, August 17, 1920. 



